Numerical analysis of NH₃-CH₄-air mixing quality effects on NO_x formation in an air-staged gas turbine model combustor

Abstract

NH₃ has emerged as a promising candidate for low-carbon gas turbines, with NO_x emission issues being mitigated by air-staged combustion. However, the role of fuel/air mixing quality (represented by unmixedness) in NO_x formation in NH₃ systems remains poorly explored. In this study, the characteristics of NO_x formation under the effects of unmixedness have been numerically investigated using an NH₃/CH₄ fired air-staged model combustor consisting of perfectly stirred reactors (PSRs) and plug flow reactors (PFRs), employing the 84-species, 703-reaction Tian mechanism under H/J heavy duty gas turbine conditions. It was found that a primary-stage equivalence ratio of 1.2–1.5 corresponds to a low NO_x formation region under perfectly mixed fuel and air conditions. In this region, a relatively low NO_x formation is achieved when the unmixedness is less than 0.12 and NO_x formation exhibits low sensitivity to fuel/air unmixedness. Based on these findings and the fact that the air-staged combustion loses its advantage in reducing NO_x emissions when the unmixedness exceeds 0.12 across all equivalence ratios, recommended mixing quality thresholds for different equivalence ratios are proposed to guide combustor design and operation optimization. A parametric study of chemical reaction pathways at different unmixedness levels in the two stages demonstrates that NO_x is mainly formed in the main combustion zone of the secondary stage via the HNO pathway, which results in NO_x formation rising to thousand ppm when unmixedness exceeds 0.3, although NO_x reduction through NHi and N₂O pathways partially offsets contributions from the HNO and thermal NO_x pathways. To leverage the NO_x reduction potential of the NHi and N₂O pathways, the residence time in both stages should be carefully adjusted to help suppress NO_x to as low as 48 ppm. The results of this study are important for engineering applications, providing guidance for the design of NH₃ fired combustors aimed at significantly reducing NO_x formation.

Graphical abstract

Keywords

NH₃ fired combustion / unmixedness / perfectly stirred reactor (PSR) / plug flow reactor (PFR) / NO_x formation / air-staged combustion

1 Introduction

Thanks to the global push for carbon neutrality and carbon peaking to combat climate change, ammonia (NH₃)—a carbon-free fuel—has been reconsidered as an alternative fuel for gas turbines due to its relatively high energy density, easy transportation, and convenient storage [1,2]. In recent years, investigations on NH₃-fueled gas turbine have surged, with combustion characteristics such as autoignition and flame propagation systematically studied through experiments and simulations [3–7]. For example, Shu et al. [8] investigated the flame propagation properties of NH₃/methane (CH₄)/air mixtures using outwardly expanding spherical flames in a constant-pressure chamber, with CH₄ volume ratios ranging from 0.1 to 0.9 and equivalence ratios from 0.6 to 1.4. Somarathne [9] reported that premixed NH₃/air combustion could be stabilized in intensive swirl combustors lower mixture velocities, resulting in longer residence time for the fuel consumption. The evolution of NH₃ chemical reaction mechanisms have been explored by Alnasif et al. [10], highlighting that current chemical reaction mechanisms are limited to specific combustion conditions and remain under development.

Although pure NH₃ has been proven to be viable for micro gas turbines [11,12], it is generally recommended to blend NH₃ with CH₄ or hydrogen (H₂) to stabilize combustion, due to the high minimum ignition energy (MIE) and low burning velocity of NH₃ [13,14]. The maximum unstretched laminar burning velocity of NH₃ is less than 7 cm/s at pressures from ambient to 0.5 MPa and equivalence ratios from 0.7 to 1.3, which is lower than those of hydrocarbon and hydrogen [15].

One challenge hindering the widespread use of NH₃ as a fuel is its N-bound nature, which can result in excessive formation of fuel NO_x [15‒18]. The NO_x formation characteristics in NH₃ combustion have been studied systematically by Kobayashi’s group in Japan [6,15,19‒23], contributing to engineering advances in NH₃-fueled gas turbines. Initially, NO_x emissions in NH₃ combustion were managed using post-processing device [24], such as selective catalytic reduction (SCR), with emissions limited to 10 ppm [19]. While post-treatment techniques such as SCR and selective non-catalytic reduction (SNCR) can reduce NO_x, they increase installation and maintenance costs. This has motivated researchers to explore proactive pollution prevention methods, focusing on combustion organizations for NO_x control in NH₃-fueled gas turbines [25].

Air-staged combustion has been proven to be an efficient way for NO_x reduction [26–28]. Li et al. [29] demonstrated that air-staged combustion, implemented through simplified model combustors, is a realistic approach to suppress NO_x formation. Detailed studies of different chemical pathways in the both single-stage and air-staged systems—perfectly stirred reactors (PSRs) to represent the main combustion zone and PFRs for the post-combustion zone—have shown that NO_x mainly forms in the main combustion zone via the HNO pathway. Air-staged combustion can further reduce NO_x emissions through NHi (NH₂ + NH) pathways in the fuel-rich primary stage. Xue et al. [30] numerically analyzed NO_x formation in NH₃/H₂/air mixtures in PSRs using four different chemical mechanisms under low-temperature chemistry, and proposed a multi-staged low-temperature combustion system for lean NH₃/H₂/air mixtures. Rocha et al. [18] compared different NH₃ combustion strategies and found that rich-burn, quick-quench, lean-burn (RQL) configurations offer stable combustion under fuel-rich conditions while producing low NO_x. As studies have shown, NO_x is depressed when the equivalence ratio exceeds 1 [22,31,32], making air-staged combustion an effective method to control NO_x by creating a fuel-rich primary stage followed by a fuel-lean secondary stage [22,33,34]. Pan et al. [28] showed that complete combustion of NH₃ and CH₄, with low NO_x and CO emissions, can be achieved in air-staged combustion with a primary stage equivalence ratio of 1.2 and an overall equivalence ratio of 0.6.

The unmixedness of fuel and oxygen has been proven to significantly affect NO_x formation [35–37]. Seo et al. [38] experimentally studied the normalized unmixedness of natural gas (> 95% methane) and air in a model combustor, finding that the unmixedness (defined as the root mean square of mixture fraction over the mean) at the inlet of the model combustor decays from an initial value of about 0.33. Wiranegara et al. [35] experimentally studied the effects of unmixedness on NO_x formation in a dry low-NO_x combustor with CH₄ as fuel at elevated pressure, concluding that better mixing (aided by higher turbulence) reduces NO_x emissions. Okafor et al. [39] experimentally and numerically studied NO_x formation in a pure NH₃ fired micro gas turbine with air-staged combustions (ignited by H₂), achieving NO_x emission of 42 ppm and combustion efficiency of 99.5% at 304.0 kPa and 298 K. Their results confirmed that NO_x formation is highly affected by mixture uniformity, with lower NO_x emission observed in premixed rather than non-premixed conditions. Li et al. [40] used a chemical-reactor-network (CRN) model to study the effects of inter-stage mixing on NO_x emissions in an NH₃-rich/lean staged combustion system in an E-class model combustor, and found that NO_x formation is highly sensitive to mixing quality at an equivalence ratio of 1.25.

Although numerous studies have focused on NH₃ combustion and NO_x formation reduction, a systematic quantitative analysis of the effect of unmixedness on NO_x formation in NH₃ combustion remains lacking. Therefore, it is of practical importance to analyze emission characteristics under varying fuel/air unmixedness in NH₃-fired staged combustion systems at H/J class gas turbine operating conditions.

This study contributes to the understanding of NO_x emission in NH₃/CH₄/air combustion for gas turbines through a systematic study of NO_x formation mechanisms over a wide range of equivalence ratios and NH₃ dilution ratios, considering the effect of fuel/air unmixedness. The conclusions may serve as useful guidelines for the design of combustors and fuel nozzle. Section 2 details the construction of the NH₃/CH₄-fired air-staged model combustor and the contributions of unmixedness on NO_x formation. Section 3 presents a quantitative discussion on the effects of unmixedness in the air-staged model combustion system. Conclusions are provided in Section 4.

2 Methodology

The staged combustion system consists of primary and secondary combustion stages. Constructing a chemical reactor network (CRN) using PSRs and PFRs is a common and effective approach for studying the emission characteristics of combustors, and has been successfully applied in numerous studies [25,41,42]. In this study, the main combustion zone of each stage is modeled by a PSR, while the post-combustion zone is represented by a PFR, as sketched in Fig. 1. It should be noted that in Fig. 1 the primary stage consists of one PSR and one PFR, under the assumption of perfect fuel-air mixing.

The NO_x formation under the influence of fuel/air unmixedness is analyzed for the operating conditions of H/J class heavy-duty gas turbines, with the unburned mixture temperature set at 647 K, the combustor outlet temperature fixed at 1873 K, and the pressure at 2.33 MPa [43]. Higher temperature and pressure conditions are not considered in this study, as the H/J class turbine parameters—1873 K and 2.33 MPa—represent the upper bound for practical engineering applications. Residence time is one of the most critical parameters in predicting NO_x emissions in gas turbine combustors. In this study, the residence times are chosen to reflect typical values found in industrial gas turbines [18,29,40], with a total combustor residence time of approximately 20 ms, and several milliseconds allocated to the main combustion zone. Continuing from previous work [29], the same residence times are adopted: 3 ms for each PSR and 10 ms for each PFR in both the primary and secondary stages, unless otherwise specified. The CHEMKIN PSR and PFR modules are employed for calculations.

Among various chemical mechanisms, such as the Konov mechanism, the Tian mechanism has demonstrated more conservative results and superior accuracy for NO_x prediction under fuel-rich conditions [31]. Therefore, the Tian mechanism, which includes 84 species [44], is used in this study to analyze NO_x formation characteristics. In this context, NO_x refers to the sum of NO and NO₂, unless otherwise stated.

Currently, the majority of gas turbines operate on natural gas. The transition to hydrogen-fueled turbines poses technical challenges and requires further development. A staged transition pathway for gas turbine fuels should involve ① natural gas→② natural gas and alternative low-carbon fuels (such as NH₃)→③ alternative low-carbon fuels with hydrogen→④ pure hydrogen.

This study focuses on the second step, examining the combustion characteristics of CH₄ and NH₃ mixtures to inform future gas turbine design.

In the staged combustion system, the global composition of the unburned mixture can be expressed as

(1)\varphi \left[\eta {\mathrm{N}\mathrm{H}}_3+\left(1-\eta \right){\mathrm{C}\mathrm{H}}_4\right]+\left(2-5/4\eta \right)({\mathrm{O}}_2+3.76{\mathrm{N}}_2),

where \varphi is the global equivalence ratio, \eta is the volume ratio of NH₃ in the fuel. The main variables in the staged combustion system are the equivalence ratio in the primary stage {\varphi }^{1\mathrm{s}\mathrm{t}}, the volume ratio of NH₃ in fuel \eta, and the distribution of residence time between the two stages. The global equivalence ratio is constrained by the requirement to maintain a combustor outlet temperature of 1873 K.

For different values of {\varphi }^{1\mathrm{s}\mathrm{t}} and NH₃ in fuel \eta, the inlet mass fraction of species for the primary and the secondary stages are shown in Fig. 2, where the horizontal axis represents {\varphi }^{1\mathrm{s}\mathrm{t}} and the vertical axis represents \eta. To maintain the outlet temperature at 1873 K, the global equivalence ratio varies from 0.52 to 0.59 depending on \eta, and remains relatively constant across different values of {\varphi }^{1\mathrm{s}\mathrm{t}} at fixed \eta. This behavior reflects nonlinearities caused by manually adjusting the air mass flow rate into the secondary stage. The mass fraction of O₂ in the secondary stage Y_{{\mathrm{O}}_2}^{2\mathrm{n}\mathrm{d}} decreases slightly with \eta when the equivalence ratio in the primary stage is larger than 1.0 as the global equivalence ratio increases to offset the lower enthalpy induced by the higher content of NH₃.

The NO_x emission performance of the staged combustion system, under the assumption of perfectly mixed fuel and air, is shown in Fig. 3, with different equivalence ratio in the primary stage against the volume ratio of NH₃ in the fuel. As illustrated by the deep blue region in the contour of Fig. 3(a), it is evident that when the equivalence ratio in the primary stage ranges from 1.2 to 1.5, NO_x formation is significantly lower. For instance, NO_x emissions are below 97 ppm when the equivalence ratio in the primary stage is 1.5 and volume ratio of NH₃ is 40%, which meets the standard for air pollutants from boilers in China (GB 13271-2014). In contrast, NO_x emissions exceed 450 ppm outside this equivalence ratio, primarily due to the dominant contribution of the HNO reaction pathway in the presence of unconverted NH₃.

In Fig. 3(b), NO_x formation within the equivalence ratio range of 1.2–1.5 in the primary stage is plotted as a function of \eta (NH₃ volume ratio). It can be noticed that lower equivalence ratios within the range results in reduced sensitivity of NO_x formation to the NH₃ ratio in the fuel. Therefore, supposed that the mixing between fuel and air is ideal, appropriate equivalence ratios can be recommended for a given NH₃ fuel ratio base on the trends presented in Figs. 3(a) and 3(b).

However, the blend of fuel and air is not uniform in most real combustors. To describe the effect of fuel/air mixing on NO_x formation, the mixture fraction and unmixedness [36] are expressed as

(2)\xi =\left({\dot{m}}_{{\mathrm{N}\mathrm{H}}_3}+{\dot{m}}_{{\mathrm{C}\mathrm{H}}_4}\right)/\left({\dot{m}}_{{\mathrm{N}\mathrm{H}}_3}+{\dot{m}}_{{\mathrm{C}\mathrm{H}}_4}+{\dot{m}}_{\mathrm{a}\mathrm{i}\mathrm{r}}\right)=a/\left(a+b\right),

(3)\mu =r.\mathrm{m}.\mathrm{s}\left(\xi \right)/\tilde{\xi },

where the mixture fraction \xi is the mass fraction of unburned fuel, a is \varphi \left[\eta W_{\mathrm{N}{\mathrm{H}}_3}+\left(1-\eta \right)W_{{\mathrm{C}\mathrm{H}}_4}\right], and b is \left(2-5/4\eta \right)\left(W_{{\mathrm{O}}_2}+3.76W_{{\mathrm{N}}_2}\right); W_i is the molecular weight of the ith species. The unmixedness, as defined in Eq. (3), is the ratio of the root mean square (RMS) of the mixture fraction to its mean value (\tilde{\xi }). This metric quantifies the deviation of the mixing quality of fuel and air. When the unmixedness is zero, it indicates perfect mixing between fuel and air mix. In this study, the effects of unmixedness on NO_x formation are incorporated through the probability density function (PDF) of the mixture fraction

(4){\tilde{X}}_{{\mathrm{N}\mathrm{O}}_x}\left(\tilde{\xi },\mu \right)={\int }_0^1{X}_{{\mathrm{N}\mathrm{O}}_x}\left(\xi \right)f\left(\xi ;\tilde{\xi },\mu \right)\mathrm{d}\xi ,

where {\tilde{X}}_{{\mathrm{N}\mathrm{O}}_x} is the mean NO_x formation and f\left(\xi ;\tilde{\xi },\mu \right) is the PDF of mixture fraction. The distribution of the PDF of the mixture fraction plays a crucial role in NO_x emissions, particularly in terms of the characteristics of fuel/air mixing. The β PDF is usually used to represent the PDF of the mixture fraction [45]. The formula and diagram for the β PDF are shown below. It is evident that when the unmixedness is 0.2, the quality of fuel and oxidizer mixing is relatively low.

(5)f\left(\xi ;\alpha ,\beta \right)=\frac{\mathrm{\Gamma }\left(\alpha +\beta \right)}{\left[\mathrm{\Gamma }\left(\alpha \right)\mathrm{\Gamma }\left(\beta \right)\right]{\xi }^{\alpha -1}{\left(1-\xi \right)}^{\beta -1}},

where α and β are the functions of \tilde{\xi } and \mu in this study.

Assuming perfect mixing between the combustion products from the primary stage and the fresh air introduced in the secondary stage, enabled by large amount of air injection into the combustor, the effects of unmixedness in this study are modeled by introducing a species distribution in the primary stage, as sketched in Fig. 5. The mean values of key parameters, such as species and temperature at the outlet of the primary stage, are used as the inlet conditions for the secondary stage.

3 Results and discussion

3.1 Overall effects of unmixedness on NO_x formation

In this section, based on Fig. 3(b), it is observed that the slope of NO_x emission begins to rise significantly at an NH₃ volume ratio of 40% when the equivalence ratio in the primary stage is 1.5. Therefore, conditions with 40% NH₃ are selected for the detailed investigation of NO_x formation characteristics under the influence of unmixedness. As shown in Fig. 3(a), with a fixed nonzero NH₃ volume ratio η, NO_x emissions first decrease, then remain at a relatively low level, and eventually rise to thousand ppm. Considering that the β PDF is essentially a weighted average, and that NO_x trends with equivalence ratio are similar across different fuel compositions, it can be inferred that the general behavior of NO_x versus unmixedness, as modeled by the β PDF, should be consistent for other volume ratios of NH₃ as well.

Figure 5 shows the contour of NO_x emissions in the staged combustion system as a function of unmixedness across different equivalence ratios in the primary stage. NO_x emissions for equivalence ratios in the primary stage between 1.2 and 1.5 are more sensitive to the changes in unmixedness, aligning with the findings in Li et al. [40], which reported heightened sensitivity of NO_x formation to mixing quality at an equivalence ratio of 1.25. When the equivalence ratio is either 1.0 or 2.0, NO_x concentrations are approximately 1000 ppm, and their sensitivity to fuel/air unmixedness is relatively low.

When unmixedness exceeds 0.12, the benefits of air-staged combustion for NO_x reduction are lost compared to a non-staged, lean NH₃ premixed combustion system, regardless of the equivalence ratio in the primary stage. Under higher unmixedness conditions with an equivalence ratio of 1.5 in the primary stage, a substantial amount of NO_x formed in the main combustion zone in the primary stage cannot be effectively reduced in the secondary stage. For the case with the equivalence ratio of 2.0 in the primary stage, NH₃ cannot be fully consumed in the primary stage, and fuel-bound NO_x is mainly formed in the main combustion zone in the secondary stage through NH₃ oxidation.

Table 1 lists the recommended unmixedness at different equivalence ratios in the primary stage based on Fig. 6. These values can serve as a reference for the structural and operating condition design of nozzles and combustors.

3.2 Analysis of effects of unmixedness

To construct the β PDF quantifying the effects of unmixedness on NO_x formation in staged NH₃ combustion, the equivalence ratio is restricted to the range of 1.0 to 2.0, and unmixedness is limited to a maximum value of 0.1 to ensure that staged combustion remains effective in reducing NO_x emissions (as depicted in Fig. 6). The PDFs with a mean equivalence ratio in the primary stage of 1.5, over the range of unmixedness from 0.02 to 0.1, are presented in Fig. 7. The PDFs for different unmixedness levels used in this study as a function of equivalence ratio are illustrated in Fig. 7, while the distribution features of PDFs with unmixedness over mixture fraction are shown in Fig. 4.

The equivalence ratio of 1.5 in the primary stage is used as an example for the analysis below. As shown in Fig. 8(a), NO_x concentrations in ppm at the outlet of both the primary and secondary stages are compared for different unmixedness conditions. It is observed that NO_x formation in the primary stage does not increase with unmixedness until it exceeds 0.1 and the majority of NO_x in the air-staged combustion system is formed in the secondary stage. This trend is also observed for equivalence ratios of 1.4, 1.3, and 1.2, as illustrated in Figs. 8(b)‒8(d). Since a significant amount of NO_x is formed in the main combustion zone of the secondary stage and increases with unmixedness, the fuel/air mixing quality should be given serious consideration in the design of air-staged systems.

It is worth noting that N₂O has received increasing attention due to its role as a potent greenhouse gas with a significant impact on global warming. As shown in Fig. 9, N₂O formation increases monotonically with unmixedness in the primary stage, while in the secondary stage, it initially increases and then decreases. Compared to the NO_x formation characteristics shown in Fig. 8(a), the concentration of N₂O is much lower, remaining below 1 ppm across the range of unmixedness. Therefore, N₂O formation in the NH₃-fired air-staged model combustor is not a major concern from a pollutant emissions standpoint.

To reveal the underlying reason of the increase in NO_x formation with rising unmixedness, further analysis was performed on the NO_x production rate from different reaction pathways, as well as the distribution of key radicals involved NO_x formation. Since NO constitutes approximately 99% of NO_x, the analysis focuses on the reaction pathways contributing to NO formation [29]. In NH₃/CH₄/air combustion, the main pathways for NO formation are classified into four categories: the HNO pathway, the thermal NO pathway, the NHi pathway (involving NH₂ and NH), and the N₂O pathway, as summarized in Table 2 [29].

Recent updates on N₂O formation mechanisms have been proposed by Glarborg et al. [4] who introduced revised chemical pathways for N₂O chemistry at pressures around 10.1 MPa and temperatures from 600 to 925 K. While these revised pathways may improve the accuracy of N₂O predictions under certain conditions, their impacts on the total amount of NO_x emission are expected to be limited. Under the high-temperature and high-pressure conditions typical of H/J-class heavy-duty gas turbines, NO_x formation is predominantly driven by the thermal and HNO pathways during NH₃ combustion.

The net NO_x formations in the main and post-combustion zones of both the primary and the secondary stages are shown in Fig. 10(a), where a reduction in NO_x is still observed in the post-combustion zone of the primary stage due to the fuel-rich environment. When the unmixedness is below 0.1, its impact on net NO_x formation in the main combustion zone of the primary stage is minimal, resulting in nearly unchanged NO_x levels at the outlet of the primary stage, as also shown in Fig. 8. However, for unmixedness values greater than 0.1, NO_x formation increases significantly because the amount generated in the main combustion zone outweighs the reduction of NO_x in the post-combustion zone of the primary stage. In the secondary stage, NO_x is mainly formed in the main combustion zone, where remaining N-containing species, such as NH₃ and HNO, are rapidly oxidized into NO_x.

Since most NO_x is formed mainly in the secondary stage, the analysis of NO_x formation rate and radical distributions are focused in the secondary stage in Fig. 10(b). The evolution of the net reaction rate of NO_x formation in the post-combustion zone of the secondary stage in Fig. 10(b) illustrates that the NO_x formation rate initially decreases and then increases with unmixedness in the main combustion zone (i.e., at the PFR inlet, residence time = 0). When the unmixedness is around 0.03, the NO_x formation rate reaches a minimum. This is likely because the equivalence ratio distribution is concentrated around 1.3–1.7, a range associated with low average NO_x formation. Downstream along the PFR in the secondary stage, the NO_x formation rate rapidly decreases and stabilizes in the post-combustion zone.

The NO_x formation rates for four key reaction pathways, HNO, thermal NO_x, NHi and N₂O, are shown in Fig. 11, based on rate-of-production analysis. Among these, the HNO pathway is the dominant contributor to NO_x formation in the main combustion zone of the secondary stage. To quantify the contribution of each pathway, an indicator is defined as {\alpha }_i={\omega }_i/\sum _i^n{\omega }_i, in which {\omega }_i is the reaction rate of the ith chemical reaction pathway. It found that the HNO + O₂ → NO + HO₂ is the most significant contributor in the main combustion zone of the secondary stage, with α values ranging from 31% to 79% as unmixedness increases from 0.02 to 0.4.

When the unmixedness is below 0.05, the NO_x formation rates for the HNO, NHi, N₂O, and thermal NO_x pathways all maintain relatively low. As unmixedness increases, the NO_x formation rates via the HNO and thermal NO_x pathways rise significantly in the main combustion zone of the secondary stage. In contrast, the NHi and N₂O pathways begin to exhibit negative contributions, partially offsetting the NO_x generated by the HNO and thermal NO_x pathways. Nevertheless, the net NO_x formation rate in the main combustion zone continues to increase with higher unmixedness, as shown in Fig. 10(b).

In the post-combustion zone of the secondary stage, NO_x formation is primarily driven by the N₂O and thermal NO_x pathways. For example, under conditions with an unmixedness of 0.1, the NO_x formation rates through the N₂O and thermal NO_x pathways reach 0.21⁶ and 0.32 ppm/ms, respectively, at 0.5 ms. In comparison, the NO_x formation rates form the HNO and NHi pathways are significantly lower, at 0.011 and 0.007 ppm/ms, respectively.

Radical distributions are explored to reveal the variation of NO_x formation rates with unmixedness and residence time. Key radicals and intermediate species, HNO, NHi, N₂O, OH, O, and H, are known to play crucial roles in NO_x formation. Accordingly, the concentrations of these species are investigated in both the primary and secondary combustion stages.

Figure 12(a) illustrates the mass fractions of critical N-containing species, NHi (a major contributor to NO_x reduction), HNO (a key precursor of NO_x in NH₃ combustion), and N₂O (another contributor to NO_x reduction), at the outlet of the primary stage, which serves as the inlet of the secondary stage. It is observed that the mass fraction of HNO at the outlet of the primary stage slightly decreases when unmixedness is below 0.1, indicating a reduction in its contribution to NO_x formation. Conversely, the mass fractions of NHi and N₂O, which is critical to the reduction of NO_x, the mass fraction of residual NHi and N₂O in the primary stage increases with unmixedness.

In the secondary stage, the increase in residual NH₃—resulting from elevated unmixedness in the primary stage—leads to a corresponding increase in NO_x formation, consistent with the trends shown in Fig. 5. Figure 12(b) presents the mass fractions of key radicals responsible for thermal NO_x formation at the outlet of the primary stage. Among these, OH has the highest concentration, exceeding those of the N-containing species shown in Fig. 12(a). The influence of unmixedness on the mass fractions of H and N is relatively minor, particularly when compared to its effects on OH and O.

In the secondary stage, the thermal NO_x formation rate is found to increase with unmixedness, primarily due to higher concentrations of reactive radicals like OH and O in the main combustion zone.

The evolutions of the mass fraction of N-containing critical species in the post-combustion zone of the secondary stage under different unmixedness conditions are shown in Fig. 13(a). The influence of unmixedness on the distribution of these species is most significant at the beginning of the post-combustion zone. Although the mass fractions of NHi and N₂O are higher than the one of HNO, their contributions to NO_x reduction are comparatively smaller, as shown in Fig. 11. Additionally, when unmixedness is below 0.05, the mass fractions of N-containing species are lower, indicating reduced fuel-bound NO_x formation.

The mass fractions of critical species for thermal NO_x formation are depicted in Fig. 13(b). The concentrations of radicals OH, O, and H decrease with increasing unmixedness. For instance, the mass fraction of OH drops from 0.000338 at an unmixedness of 0.04 to 0.000288 at 0.3. The N radical initially decreases and then increases with unmixedness, which is consistent with the trend of thermal NO_x formation shown in Fig. 11. Overall, the mass fractions of radicals OH, O, and, H—key contributors to thermal NO_x—are significantly higher than those of fuel-bound NO_x precursors such as HNO. This demonstrates that thermal NO_x is the dominant formation pathway in the post-combustion zone of the secondary stage.

3.3 Performance with different allocations of residence time

It has been pointed in Li et al. [29] that the allocation of residence time has a significant effect on NO_x formation under perfect fuel/air mixing conditions. By maintaining a total residence time of 20 ms in the post-combustion zone of both stages, increasing the residence time in the post-combustion zone can further reduce NO_x formation. This is because more NO_x can be reduced in the post-combustion zone through the NHi and N₂O pathways.

The performance of NO_x formation with different residence time allocations in the primary stage, in the presence of fuel/air unmixedness at the inlet, is displayed in Fig. 14(a). As unmixedness increases, NO_x formation decreases with longer residence time in the post-combustion zone of the primary stage, since the reduction of NO_x through the NHi and N₂O pathways is more pronounced in the post-combustion zone of the primary stage. However, the effects of residence time allocation on NO_x formation are negligible at the outlet of the primary stage.

Figure 14(b) illustrates the effects of unmixedness on N-containing species and are directly reflected in the profiles of total NO_x formation in the air-staged combustion system. The difference in NO_x formation with varying residence times in the post-combustion zone of the primary stage is more significant at lower unmixedness levels. When unmixedness is 0, NO_x formation decreases from 125 to 13 ppm, as residence time increases from 8 to 18 ms. In contrast, when unmixedness is 0.04, NO_x formation decreases from 228 to 48 ppm. As unmixedness increases, the difference in NO_x formation across various residence time allocations becomes increasingly smaller. Based on these findings, careful allocation of residence time in both stages can help maintain NO_x emissions at relatively low levels.

4 Conclusions

The effects of unmixedness on NO_x emission characteristics have been numerically investigated in an NH₃/CH₄-fired air-staged model combustor, consisting of PSRs and PFRs, using the 84-species Tian mechanism under typical H/J heavy duty gas turbines conditions, (2.33 MPa and 1873 K). In this study, the recommended equivalence ratio for the primary stage and the upper boundary of fuel/air unmixedness for low-NO_x air-staged combustion, with a 40% volume ratio of NH₃ in the fuel, are presented to guide combustor structure design and optimize operational processes. The main conclusions are as follows:

1) Low NO_x formation at optimal equivalence ratios: NO_x formation remains low when the equivalence ratio in the primary stage is between 1.2 and 1.5 under perfectly fuel/air mixing conditions. In this range, NO_x formation in the primary stage is insensitive to fuel/air mixing quality when the unmixedness is below 0.12.

2) Impact of unmixedness on NO_x reduction: When unmixedness exceeds 0.12, the air-staged combustion system loses its advantage in NO_x emission reduction for NH₃/CH₄/air combustion with 40% NH₃ dilution at 2.33 MPa, and a residence time of 10 ms in the post-flame region of the primary stage. This underscores the necessity for precise mixing uniformity to achieve effective NO_x suppression in gas turbine combustors.

3) Nonlinear effects of unmixedness on NO_x formation: The effect of unmixedness on the NO_x formation rate are nonlinear, with the majority of NO_x formed in the main combustion zone of the secondary stage via the HNO pathway. When unmixedness exceeds 0.3, NO_x formation rises to thousand ppm, although the NO_x reduction via the NHi and N₂O pathways partially offsets the increase in HNO and thermal NO_x pathways.

4) Strategies for further NO_x reduction: By carefully controlling fuel and air mixing, as well as optimizing the allocation of residence time in the two stages, NO_x emissions can be further reduced and maintained at relatively low levels. For example, NO_x can be reduced to 48 ppm with an unmixedness of 0.04 and a residence time of 18 ms in the post-combustion zone of the primary stage. This provides a practical strategy for further reducing NO_x formation in NH₃-fired combustors.

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